\documentclass[
	solutions,
	singlenumbering,
	nopagenumber
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}


\makeatletter
\newcommand{\thisone}{
	\if@solutions
	{\color{red} $\Leftarrow$ \texttt{this one}}
	\else\fi
}

\title{Zeno's Furniture}
\uptitlel{Warm Ups}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today}

\begin{document}

	\maketitle

	Zeno Furniture sells exactly five types of furniture:
	\begin{itemize}
		\item Footstools
		\item Hutches
		\item Sideboards
		\item Tables
		\item Vanities
	\end{itemize}
	Irene buys four items, each of a different type,
	and each made of exactly one kind of wood:
	\begin{itemize}
		\item Maple
		\item Oak
		\item Pine
		\item Rosewood
	\end{itemize}

	The following conditions govern Irene's purchases:
	\begin{itemize}
		\item Any vanity she buys is Maple.
		\item Any rosewood item she buys is a sideboard.
		\item If she buys a vanity, she does not buy a footstool.
		\item If she buys a footstool, she also buys a table made of the same material.
		\item Irene does not buy an oak table.
		\item Exactly two of the items she buys are made of the same kind of wood.
	\end{itemize}




	\problem{}
	Which one of the following could be an accurate
	list of the items Irene buys? \par
	\begin{itemize}
		\item maple footstool, maple hutch, rosewood sideboard, maple table
		\item oak hutch, rosewood sideboard, pine table, oak vanity
		\item rosewood hutch, maple sideboard, oak table, maple vanity
		\item pine footstool, rosewood sideboard, pine table, maple vanity
		\item maple footstool, pine hutch, oak sideboard, maple table \thisone{}
	\end{itemize}
	\vfill


	\problem{}
	If Irene buys one item made of rosewood and two items made
	of maple, then which one of the following pairs could be two
	of the items she buys?
	\begin{itemize}
		\item a rosewood sideboard and an oak footstool
		\item an oak hutch and a pine sideboard
		\item an oak hutch and a maple table \thisone{}
		\item a maple sideboard and a maple vanity
		\item a maple hutch and a maple table
	\end{itemize}
	\vfill
	\pagebreak


	\problem{}
	Which one of the following is a complete and accurate list
	of all the woods any footstool that Irene buys could be made of?
	\begin{itemize}
		\item maple, oak
		\item maple, pine \thisone{}
		\item maple, rosewood
		\item maple, oak, pine
		\item maple, oak, pine, rosewood
	\end{itemize}
	\vfill


	\problem{}
	Suppose Irene buys a footstool. Then which one of the following
	is a complete and accurate list of items and any one of which she
	could buy in maple?
	\begin{itemize}
		\item footstool, hutch, sideboard, table, vanity
		\item footstool, hutch, sideboard, table \thisone{}
		\item footstool, hutch, sideboard
		\item footstool, hutch
		\item footstool
	\end{itemize}
	\vfill

	\problem{}
	Which one of the following cannot be the two items Irene
	buys that are made of the same wood as each other?
	\begin{itemize}
		\item footstool, hutch \thisone{}
		\item hutch, sideboard
		\item hutch, table
		\item sideboard, vanity
		\item table, vanity
	\end{itemize}
	\vfill
	\pagebreak

	\problem{}
	If Irene does not buy an item made of maple, then each of the
	following must be true except...
	\begin{itemize}
		\item Irene buys a footstool
		\item Irene buys a pine hutch \thisone{}
		\item Irene buys a rosewood sideboard
		\item Irene buys exactly one item made of oak
		\item Irene buys exactly two items made of pine
	\end{itemize}
	\vfill


	\problem{}
	Suppose the condition that Irene does not buy an oak table is
	replaced with the condition that she does not buy a pine table.
	If all the other conditions hold as originally given, which of the
	following cannot be true?
	\begin{itemize}
		\item Irene buys an oak footstool.
		\item Irene buys a hutch and a table made of the same wood.
		\item Irene buys a vanity, but she does not buy an oak table.
		\item Irene buys a maple table and an oak hutch.
		\item Irene buys a rosewood sideboard and exactly two items made of pine. \thisone{}
	\end{itemize}
	\vfill
	\pagebreak

\end{document}